An extension of the stochastic sewing lemma and applications to fractional stochastic calculus
Forum of Mathematics, SigmaWe give an extension of Lê’s stochastic sewing lemma. The stochastic sewing lemma proves convergence in $L_m$ of Riemann type sums $\sum _{[s,t] \in \pi } A_{s,t}$ for an adapted two-parameter stochastic process A, under certain conditions ...
Toyomu Matsuda, Nicolas Perkowski
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Robust option replication for a Black-Scholes model extended with nondeterministic trends [PDF]
, 2012 Statistical analysis on various stocks reveals long range dependence behavior of the stock prices that is not consistent with the classical Black and Scholes model.
Kloeden, Peter E. +1 more
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Averaging principle for equation driven by a stochastic measure
, 2018 Equation with the symmetric integral with respect to stochastic measure is considered. For the integrator, we assume only $\sigma$-additivity in probability and continuity of the paths.
Radchenko, Vadym
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Multiple G-Stratonovich integral in G-expectation space
Open MathematicsThe Stratonovich integral represents a fundamental concept in stochastic calculus. In this article, we first propose a novel approach inspired by the multidimensional G-Itô formula, establishing a multiple G-Stratonovich integral within the G-expectation
Fei Shaojin
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A Distributed Procedure for Computing Stochastic Expansions with Mathematica [PDF]
, 2010 The solution of a (stochastic) differential equation can be locally approximated by a (stochastic) expansion. If the vector field of the differential equation is a polynomial, the corresponding expansion is a linear combination of iterated integrals of ...
Ladroue, Christophe +1 more
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On the weak convergence of multiparameter stochastic integrals
Open MathematicsIn this paper we provide sufficient conditions for sequences of stochastic processes of the form ∫ [0,t] f n(u)θ n(u)du, to weakly converge, in the space of continuous functions over a closed interval, to integrals with respect to the Brownian motion, ∫ [
Bardina Xavier, Boukfal Salim
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On the excursions of drifted Brownian motion and the successive passage times of Brownian motion
, 2016 By using the law of the excursions of Brownian motion with drift, we find the distribution of the $n-$th passage time of Brownian motion through a straight line $S(t)= a + bt.$ In the special case when $b = 0,$ we extend the result to a space-time ...
Abundo, Mario
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Optimal insider control and semimartingale decompositions under enlargement of filtration
, 2016 We combine stochastic control methods, white noise analysis and Hida-Malliavin calculus applied to the Donsker delta functional to obtain new representations of semimartingale decompositions under enlargement of filtrations.
Draouil, Olfa, Øksendal, Bernt
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An extension of Wiener integration with the use of operator theory
, 2009 With the use of tensor product of Hilbert space, and a diagonalization procedure from operator theory, we derive an approximation formula for a general class of stochastic integrals.
Ash R. B. +9 more
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Stochastic Volterra equations driven by cylindrical Wiener process
, 2007 In this paper, stochastic Volterra equations driven by cylindrical Wiener process in Hilbert space are investigated. Sufficient conditions for existence of strong solutions are given.
Karczewska, Anna, Lizama, Carlos
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