Generalized stochastic integrals and equations
نویسندگان
چکیده
منابع مشابه
Generalized Integrals and Differential Equations.
in which a and b are continuously differentiate functions of two variables, fix) a continuously difierentiable function. The routine estimate of fadb gives bounds depending either on /| d/(x) | or on the maximum of | df/dx\ in the interval of integration. It is, however, possible, as shown in Theorem 1, to give a bound that is entirely independent'of the derivative of fix), and, consequently, t...
متن کاملGeneralized Elliptic Integrals and Modular Equations
In geometric function theory, generalized elliptic integrals and functions arise from the Schwarz-Christoffel transformation of the upper half-plane onto a parallelogram and are naturally related to Gaussian hypergeometric functions. Certain combinations of these integrals also occur in analytic number theory in the study of Ramanujan’s modular equations and approximations to π. The authors stu...
متن کاملForward Integrals and Stochastic Differential Equations
Abstract. We show that an anticipating stochastic forward integral introduced in [8] by means of fractional calculus is an extension of other forward integrals known from the literature. The latter provide important classes of integrable processes. In particular, we investigate the deterministic case for integrands and integrators from optimal Besov spaces. Here the forward integral agrees with...
متن کاملVolterra Equations with Fractional Stochastic Integrals
We assume that a probability space (Ω,η,P) is given, where Ω denotes the space C(R+, Rk) equipped with the topology of uniform convergence on compact sets, η the Borel σ-field of Ω, and P a probability measure on Ω. Let {Wt(ω) = ω(t), t ≥ 0} be a Wiener process. For any t ≥ 0, we define ηt = σ{ω(s); s < t}∨Z, where Z denotes the class of the elements in ηt which have zero P-measure. Pardoux and...
متن کاملRough Volterra equations 2: Convolutional generalized integrals
We define and solve Volterra equations driven by a non-differentiable signal, by means of a variant of the rough path theory allowing to handle generalized integrals weighted by an exponential coefficient. The results are applied to a standard rough path x = (x,x) ∈ C 2 (R)×C 2γ 2 (R), with γ > 1/3, which includes the case of fractional Brownian motion with Hurst index H > 1/3.
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Transactions of the American Mathematical Society
سال: 1970
ISSN: 0002-9947
DOI: 10.1090/s0002-9947-1970-0261719-4