Stochastic Calculus for Fractional Brownian Motion and Related Processes

By I︠U︡lii︠a︡ S. Mishura. 2008

998 citations recorded by the source corpus.

Subfields: Economics and Econometrics, Finance

View Paper: https://www.semanticscholar.org/paper/84b337eb03c0dea0634d9a914de08c355b11c18c

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Citations in the corpus

Controlled differential equations as Young integrals: A simple approach (2010, background): “Keywords: controlled differential equations, Young integral, fractional Brownian motion, rough paths, flow property, Euler scheme.”
Surpassing the fractional derivative: Concept of the memory-dependent derivative (2011, background): “So it can be used to describe the variation of a system in which the instantaneous change rate depends on the past state, which is called the ‘‘memory effect’’ in a visualized manner [2].”
Itô's formula for a sub-fractional Brownian motion (2011, neutral): “[2], Hu [17], Mishura [19], Nualart [20].”
On drift parameter estimation in models with fractional Brownian motion (2011, methodology): “(d) It was proved in [5] that in case of non-random bounded positive function 0 ≤ θ(s) ≤ θ∗, for any stopping time υ ( E ( sup 0≤t≤υ ∣∣∣ ∫ t”
Fractional stochastic differential equations with applications to finance (2013, background): “3 in [21] we know that D(T, γ 2 ) ≤ CH‖f‖ L 1 H [0,T ] , Thus the proposition is proved.”
Fractional Backward Stochastic Differential Equations and Fractional Backward Variational Inequalities (2011, neutral): “1 [15]) yields In(Gn) = ∫ T t In(hn,s)ds = In (∫ T t hn,sds ) .”
Fractional Processes as Models in Stochastic Finance (2010, background): “Alternatively, one can build an integral on Wick-Riemann sums [6, 10, 19, 31] and examine the SDE dXt = Xtd Bt, X0 = 1.”
Rate of convergence and asymptotic error distribution of Euler approximation schemes for fractional diffusions (2014, background): “It was proved by Mishura [17] that for any real number ε > 0 there exists a random variable Cε such that almost surely, sup 0≤t≤T |X t −Xt| ≤Cεn.”
Stochastic Calculus with Respect to Gaussian Processes (2014, background): “The reader interested in an exhaustive overview of the subject may refer to [10, 37, 43] for divergence type integral and to [4, 7, 11, 42] for integral in the white noise theory framework.”