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- XIN GUO, Xin Guo, Larry Shepp, Richard Gundy
- 1999

A model of an incomplete market with the incorporation of a new notion of " inside information " is posed. The usual assumption that the stock price is Markovian is modified by adjoining a hidden Markov process to the Black-Scholes exponential Brownian motion model for stock fluctuations. The drift and volatility parameters take different values when the… (More)

Article history: Received 9 May 2012 Received in revised form 9 July 2013 Accepted 27 July 2013 Available online 2 August 2013 Communicated by Richard Gundy

We show that the H(p) spaces on the bi-disc can be characterized in terms of either the nontangential maximal function and the area integral or their probabilistic analogues resulting by introducing two-time Brownian motion (i.e., the martingale maximal function) and the corresponding square function.

- Richard F. Gundy, Kazaros Kazarian
- SIAM J. Math. Analysis
- 2000

- V Dobri´c, R Gundy, P Hitczenko, Hernández Cohen, Weiss Wang, The
- 2001

of probabilities. Abstract. The construction of a multiresolution analysis starts with the specification of a scale function. The Fourier transform of this function is defined by an infinite product. The convergence of this product is usually discussed in the context of L 2 (R). Here, we treat the convergence problem by viewing the partial products as… (More)

a r t i c l e i n f o a b s t r a c t The classical assumption in sampling and spline theories is that the input signal is square-integrable, which prevents us from applying such techniques to signals that do not decay or even grow at infinity. In this paper, we develop a sampling theory for multidimensional non-decaying signals living in weighted L p… (More)

- R Fefferman, R Gundy, M Silverstein, E M Stein
- Proceedings of the National Academy of Sciences…
- 1982

We show that the ratios (A(u)/N(u))(k)A(u) and (N(u)/A(u))(k)N(u) have L(p) norms equivalent with the H(p) norm of u. Here A(u) is the Lusin area integral and N(u) is the nontangential maximal function.

- Vladimir T. Dobric, Richard F. Gundy, Pawel Hitczenko
- SIAM J. Math. Analysis
- 2000

- Gilles Pisier, Joachim Cuntz, Richard Gundy
- 2014

We describe a new operator space structure on L p when p is an even integer and compare it with the one introduced in our previous work using complex interpolation. For the new structure, the Khintchine inequalities and Burkholder's martingale inequalities have a very natural form: the span of the Rademacher functions is completely isomorphic to the… (More)

- V Dobri´c, R F Gundy, P Hitczenko
- 2001