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Nonlinear Stochastic Differential Equations

Fully nonlinear stochastic partial differential equations: non-smooth equations and applications

Fully nonlinear stochastic partial differential equations: non-smooth equations and applications

... about equations like ...fully nonlinear character of the equations seems to make them inaccessible to the classical martingale theory employed for the linear ...the equations can not be ...

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PROBABILISTIC PROPERTIES AND PARAMETRIC INFERENCE OF SMALL VARIANCE NONLINEAR SELF-STABILIZING STOCHASTIC DIFFERENTIAL EQUATIONS

PROBABILISTIC PROPERTIES AND PARAMETRIC INFERENCE OF SMALL VARIANCE NONLINEAR SELF-STABILIZING STOCHASTIC DIFFERENTIAL EQUATIONS

... on [0,T] to (x t (α)), solution of (10). Let us consider the problem of estimating (α, β) from a continuous observation (X t , t ∈ [0, T ]). In classical stochastic differential equations with small ...

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Backward stochastic differential equations and stochastic control and applications to mathematical finance

Backward stochastic differential equations and stochastic control and applications to mathematical finance

... fully nonlinear PDE, motivated in particular by uncertain volatility model and more generally by stochastic control problem where control can affect both drift and diffusion terms of the state process, ...

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Stochastic partial differential equations with singular terminal condition

Stochastic partial differential equations with singular terminal condition

... doubly stochastic differential equations, stochastic partial differential equations, monotone condition, singular terminal ...Doubly Stochastic Differential ...

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Scaling limits and stochastic homogenization for some nonlinear parabolic equations

Scaling limits and stochastic homogenization for some nonlinear parabolic equations

... NONLINEAR PARABOLIC EQUATIONS PIERRE CARDALIAGUET, NICOLAS DIRR AND PANAGIOTIS ...form, nonlinear partial differential equation, the study of which is the second aim of the ...

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Some contributions to stochastic control and backward stochastic differential equations in finance.

Some contributions to stochastic control and backward stochastic differential equations in finance.

... fully nonlinear PDEs while standard BS- DEs induce quasi-linear ...order stochastic target problem whose solution solves a 2BSDE and prove existence and uniqueness for general 2BSDEs in [86] with an ...

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An Extension of Massera’s Theorem for N-Dimensional Stochastic Differential Equations

An Extension of Massera’s Theorem for N-Dimensional Stochastic Differential Equations

... The existence of periodic solutions for differential equations has received a particular interest. We quote the famous results of Massera [9]. In its approach, Massera was the first to establish a relation ...

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Forward-Backward Stochastic Differential Equations and Controlled McKean Vlasov Dynamics

Forward-Backward Stochastic Differential Equations and Controlled McKean Vlasov Dynamics

... of nonlinear stochastic dynamical systems of the McKean Vlasov ...the stochastic maximum principle and give sufficient conditions for existence of an optimal ...large stochastic games with ...

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Accelerated finite elements schemes for parabolic stochastic partial differential equations

Accelerated finite elements schemes for parabolic stochastic partial differential equations

... for stochastic parabolic PDEs of the form of equation ...of equations arise in various fields of sciences and engineering, for example in nonlinear filtering of partially observed diffusion ...these ...

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Scaling limits and stochastic homogenization  for some nonlinear parabolic equations

Scaling limits and stochastic homogenization for some nonlinear parabolic equations

... The assumptions on A are made for simplicity and can be relaxed. Moreover, since the coefficients of the noise in (2.1) are deterministic, the question of whether we need to use Itˆ o’s or Stratonovich stochastic ...

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Singular Forward-Backward Stochastic Differential Equations and Emissions Derivatives

Singular Forward-Backward Stochastic Differential Equations and Emissions Derivatives

... forward stochastic differential equation (SDE) for the aggregate emissions in the economy, and a backward stochastic differential equation (BSDE) for the allowance ...a nonlinear ...

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On a Wasserstein-type distance between solutions to stochastic differential equations

On a Wasserstein-type distance between solutions to stochastic differential equations

... such that P ≡ P µ,σ x 0 is the probability distribution of the unique strong solution to the stochastic differential with coefficients µ and σ and initial condition x 0 . The definition of the following ...

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Strong solutions to stochastic differential equations with rough coefficients

Strong solutions to stochastic differential equations with rough coefficients

... everywhere stochastic flows for ...Kolmogorov equations; the first one associated to the SDE ...a stochastic transport equation whose solutions are in correspondence with the stochas- tic ...

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On limit theorems and backward stochastic differential equations via Malliavin calculus

On limit theorems and backward stochastic differential equations via Malliavin calculus

... Dans cette partie de notre travail, nous mettons en oeuvre les techniques du calcul de Malliavin combinées à la méthode de Stein afin de determiner, dans un cadre gaussien, des bornes de [r] ...

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On a Wasserstein-type distance between solutions to stochastic differential equations

On a Wasserstein-type distance between solutions to stochastic differential equations

... values in the set of orthogonal matrices and converges to C ∗ (s, x, x) in L p -norm. The results below do not bring further information, either to the distance f W 2 , or to its stochastic control representation. ...

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Nonlinear damped partial differential equations and their uniform discretizations

Nonlinear damped partial differential equations and their uniform discretizations

... wave equations in the absence of geometric control condition (see [ 12 ]) but also for indirect stabilization for coupled systems, that is when certain equations are not directly stabilized, even though the ...

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Solvability for a nonlinear coupled system of n fractional differential equations

Solvability for a nonlinear coupled system of n fractional differential equations

... 2 UMAB University of Mostaganem LPAM, Faculty SEI, UMAB University of Mostaganem, Algeria Abstract In this paper, we study a nonlinear coupled system of n−fractional dif- ferential equations. Applying ...

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Forward and Backward Stochastic Differential Equations with normal constraint in law

Forward and Backward Stochastic Differential Equations with normal constraint in law

... where B is a Brownian motion, h is a function from R n to R, the law of the initial condition X 0 is such that E[h(X 0 )] ≥ 0 and where, for the time being, n = d = 1 . When focusing on this forward system, there are ...

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An eXtended Stochastic Finite Element Method for solving stochastic partial differential equations on random domains

An eXtended Stochastic Finite Element Method for solving stochastic partial differential equations on random domains

... proposed stochastic quadrature technique has given very good results since elementary matrices and vectors had a nice dependence on the random vari- ...higher stochastic dimension are key questions which ...

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Parametric inference for mixed models defined by stochastic differential equations

Parametric inference for mixed models defined by stochastic differential equations

... Our main purpose is thus to propose an efficient algorithmic estimation method of the vector of parameters θ together with theoretical convergence results. We consider an approximate statistical model, of which the ...

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