Bt + ∇b(xt )γtdt and starting from γ0, where B is a Brownian motion and σ(x)σ(x)∗ = a(x).
Structure of large random hypergraphs
C ε1 · βl e−βl tdt on [−R, R] (and zero otherwise). ii.
On a nonhierarchical version of the Generalized Random Energy Model. II. Ultrametricity
Beta(p, q |α, β ) where Γ(α) = R ∞0 tα−1 e−tdt is the Gamma function.
Exact Non-Parametric Bayesian Inference on Infinite Trees
In this case, the pdf N ft(x) (1 − Ft (x))N −1 tends to a point mass at the N ft (x) (1 − Ft (x))N −1 tdt minimum of t and the integral approaches the minimum of t.
Modulation Codes for Flash Memory Based on Load-Balancing Theory
We shall work on L2 (R, dt) on each Fourier mode, which amounts to conjugating by et/2 to pass unitarily from L2(e−tdt) to L2 (dt): let eKh := et/2Khe−t/2 and eKh,k its decomposition on the k Fourier mode fk (t) of f (t, y ).
Random walk on surfaces with hyperbolic cusps
To implement this behavior, we use the approximation Rm (z = 1 − ǫ) ≃ Rm (∞)/ǫ + R tx 1 (Rm (t) − Rm(∞))e−ǫtdt, and determine the leading behavior of Rm (z ) by comparing different time scales ǫ−1, tc, and tx .
First passage time for random walks in heterogeneous networks
Wt = W [(µρtdt + σρt dBt − γF (f )dt)] dρt = (cid:2)f + ρt (1 − ρt )(µ − σ2ρt )(cid:3) dt + [σρt (1 − ρt )] dBt + γ ρtF (f )dt For a derivation of these equations, see .
Optimal hedging of Derivatives with transaction costs
TDT) (38), but that otherwise two offspring are required.
1953: An unrecognized summit in human genetic linkage analysis
TDT (38) and other family-based association tests that may be the best hope for mapping the genes associated with complex traits.
1953: An unrecognized summit in human genetic linkage analysis
Proof: The proof makes use of the Gaussian integration by parts formula EdXσ (t)f (cid:18)Z dXσ′ (s)(cid:19) = Ef ′ (cid:18)Z dXσ′ (s)(cid:19) Z EdXσ (t)dXσ′ (s) = Ef ′ (Xσ′ ) 1IA( dist(σ,σ′ ))≥tdt where f is any differentiable function.
Rigorous results on some simple spin glass models
Fix a point realization D = L∞ (X, µ), and set XD := X × R equipped with the usual product measure dµ ⊗ e−tdt and F D t (x, s) := (x, s + t).
Amalgamated free product over Cartan subalgebra, II. Supplementary results & Examples
Ei (z) = − R ∞ −z e−tdt/t is the exponential integral function, and where the principal value of the integral must be taken.
Reheating the Universe in Braneworld Cosmological Models with bulk-brane energy transfer
Et × {t} is a measurable subset of Ω × [0, ∞) such that XE ∈ Ω XE (t) dx = m0 for al l t ≥ 0, and XE |t=0 = XE0 in L1 (Ω). (3) V is a Radon measure on Ω × Gd−1 × (0, ∞) such that V = V tdt where V t is for almost al l t ∈ (0, ∞) a general varifold on Ω, i.e., a Radon measure on Ω × Gd−1 .
Existence of weak solutions for a non-classical sharp interface model for a two-phase flow of viscous, incompressible fluids
M 2 V (m2, t) tanh(πt)tdt + O(T −A ) with A arbitrarily large.
Bounds for $GL(3)\times GL(2)$ $L$-functions and GL(3) $L$-functions
PtT = rtPtT dt + ΩtT PtT (dWt + λtdt), Here PtT is the random value at time t of the bond that matures at time T, {rt}t≥0 is the short rate, {ΩtT }T ≥t≥0 is the bond volatility, and {λt}t≥0 is the market price of risk.
Rational term structure models with geometric Levy martingales
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