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Continuity and Gaussian two-sided bounds of the density functions of the solutions to path-dependent stochastic differential equations via perturbation

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  • Kusuoka, Seiichiro

Abstract

We consider Markovian stochastic differential equations with low regular coefficients and their perturbations by adding a measurable bounded path-dependent drift term. When we assume the diffusion coefficient matrix is uniformly positive definite, then the solution to the perturbed equation is given by the Girsanov transformation of the original equation. By using the expression we obtain the Gaussian two-sided bounds and the continuity of the density function of the solution to the perturbed equation. We remark that the perturbation in the present paper is a stochastic analogue to the perturbation in the operator analysis.

Suggested Citation

  • Kusuoka, Seiichiro, 2017. "Continuity and Gaussian two-sided bounds of the density functions of the solutions to path-dependent stochastic differential equations via perturbation," Stochastic Processes and their Applications, Elsevier, vol. 127(2), pages 359-384.
    • Handle: RePEc:eee:spapps:v:127:y:2017:i:2:p:359-384
    DOI: 10.1016/j.spa.2016.06.011
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    Cited by:

    1. Mao Fabrice Djete, 2022. "Non--regular McKean--Vlasov equations and calibration problem in local stochastic volatility models," Papers 2208.09986, arXiv.org, revised Oct 2024.
    2. Naganuma, Nobuaki & Taguchi, Dai, 2020. "Malliavin calculus for non-colliding particle systems," Stochastic Processes and their Applications, Elsevier, vol. 130(4), pages 2384-2406.
    3. Mao Fabrice Djete & Gaoyue Guo & Nizar Touzi, 2023. "Mean field game of mutual holding with defaultable agents, and systemic risk," Papers 2303.07996, arXiv.org.
    4. Ngo, Hoang-Long & Taguchi, Dai, 2019. "On the Euler–Maruyama scheme for SDEs with bounded variation and Hölder continuous coefficients," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 161(C), pages 102-112.

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