Large deviation principle for diffusion processes under a sublinear expectation

Chen, ZengJing; Xiong, Jie

doi:10.1007/s11425-012-4518-4

Cited by 12 publications

(4 citation statements)

References 11 publications

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“…The model ambiguity means that the true probability measure is one taken from P. This is also equivalent to drift ambiguity because by Girsanov formula, W t ≡ W t − t 0 θ s ds is a Brownian motion and, under Q, X t is a diffusion process with drift coefficient b + σθ. For this model ambiguity, a large deviation principle is studied in Chen and Xiong [7].…”

Section: Introduction and Main Resultsmentioning

confidence: 99%

Stochastic filtering under model ambiguity

Zhang¹,

Xiong²

2022

Preprint

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In this paper, we study a non-linear filtering problem when the signal model is uncertain. The model ambiguity is characterized by a class of probability measures from which the true probability measure is taken. The optimal filter can be estimated by converting to a conditional mean field optimal control problem. In the first part of this article, we develop a general form stochastic maximum principle for a conditional mean-field type model driven by a forward and backward control system. In the second part, we characterize the ambiguity filter and prove its existence and uniqueness.

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Section: Introduction and Main Resultsmentioning

confidence: 99%

Stochastic filtering under model ambiguity

Zhang¹,

Xiong²

2022

Preprint

Self Cite

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“…Namely, when the drift and diffusion terms contain Y , by probability methods and under some suitable assumptions. Note that in [11], the authors considered the fully coupled FBSDEs via the corresponding PDE techniques.…”

Section: Introductionmentioning

confidence: 99%

“…While, with probability methods, by the contraction principle, the same small random perturbation for BSDEs and the Freidlin-Wentzell's large deviation estimates in C ([0, T ] ; R n ) are also obtained by [13,17,18,33,20] (see references therein). In [11] a large deviation principle of Freidlin and Wentzell type under nonlinear probability for diffusion processes with a small diffusion coefficient was obtained.…”

Section: Introductionmentioning

confidence: 99%

Asymptotic properties of coupled forward–backward stochastic differential equations

Cruzeiro¹,

Gomes

Zhang

2014

Stoch. Dyn.

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“…In the classical case, a variational representation of functionals of finite dimensional Brownian motion was first obtained by Boué and Dupuis ([4]). Chen and Xiong ( [7]) considered the variational representations under a g-expectation which is defined by a backward stochastic differential equation. The variational representations have been shown to be useful in deriving various asymptotic results in large deviations (cf.…”

Section: Introductionmentioning

confidence: 99%