Theory of Stochastic Differential Equations with Jumps and Applications: Mathematical and Analytical Techniques with Applications to Engineering

By R. Situ. 2005

383 citations recorded by the source corpus.

Stochastic Differential Equations with Jumps in Rd.- Martingale Theory and the Stochastic Integral for Point Processes.- Brownian Motion, Stochastic Integral and Ito's Formula.- Stochastic Differential Equations.- Some Useful Tools in Stochastic Differential Equations.- Stochastic Differential Equations with Non-Lipschitzian Coefficients.- Applications.- How to Use the Stochastic Calculus to Solve SDE.- Linear and Non-linear Filtering.- Option Pricing in a Financial Market and BSDE.- Optimal Consumption by H-J-B Equation and Lagrange Method.- Comparison Theorem and Stochastic Pathwise Control.- Stochastic Population Control and Reflecting SDE.- Maximum Principle for Stochastic Systems with Jumps.

Subfields: Finance

View Paper: https://www.semanticscholar.org/paper/1d919997aec4c5544acf2ecebf500af1fd4c6be9

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Citations in the corpus

On tamed milstein schemes of SDEs driven by Lévy noise (2014, background): “Some of the references are [2], [16], [21] and references therein.”
SDEs Driven by a Time-Changed Lévy Process and Their Associated Time-Fractional Order Pseudo-Differential Equations (2009, background): “4 [1, 24] If F(u,y) satisfies the Lipschitz and growth conditions (2.”
Continuous-State Branching Processes with Immigration (2019, background): “The reader is referred to Ikeda and Watanabe (1989) and Situ (2005) for the basic theory of stochastic equations.”
BSDEs with monotone generator driven by Brownian and Poisson noises in a general filtration (2014, background): “As in the papers of Barles et al. [1], Royer [37], Situ [38] or Quenez & Sulem [35], we have to restrict the dependence of f w.r.t. ψ .”
Finite-time stability and instability of stochastic nonlinear systems (2011, background): “Under some weaker conditions, Situ (2005) has established an existence theorem of a unique solution to (2.1).”
Ergodicity of stochastic differential equations with jumps and singular coefficients (2017, background): “We mention that the authors in [32] and [38, 44] obtained some rough Krylov’s estimates, which are not enough for our purpose.”
Yamada-Watanabe Results for Stochastic Differential Equations with Jumps (2013, methodology): “The next lemma corresponds to Fact B on page 107 in Situ [24].”
Jump type stochastic differential equations with non-Lipschitz coefficients: Non-confluence, Feller and strong Feller properties, and exponential ergodicity (2017, background): “For the convenience of later presentations, let us recall several important notions from Ikeda and Watanabe (1989) (as well as the presentations in Situ (2005)).”
Approximation properties for solutions to non‐Lipschitz stochastic differential equations with Lévy noise (2015, background): “Non-Gaussian Lévy noise with the properties of anomalous diffusion and heavy tail distribution or non-exponential relaxation may be more appropriate to model the stochastic disturbances especially with extremely large jumps, although the Gaussian white noise is widely used [9, 10].”
Optimal harvesting for a stochastic regime-switching logistic diffusion system with jumps (2014, neutral): “Rong Situ [13] (see page 32) said ''stochastic perturbation of jumps in a dynamical system usually can be modeled as a stochastic integral with respect to some point processes, i.e. its martingale measure or counting measure''.”
Refracted Lévy processes (2008, background): “159 of [14] as well as the presentation in [28].”